General Chemistry Gas Laws

							      CE 541




General Chemistry
   Gas Laws
          What Are Gas Laws


The gas laws are a set of laws that describe the
relationship between thermodynamic temperature
(T), pressure (P) and volume (V) of gases
                 Boyle's Law
Boyle's law (sometimes referred to as the Boyle
Mariotte law) is one of the gas laws.

It states that “For a fixed mass of ideal gas at fixed
temperature, the product of pressure and volume is a
constant”.
The mathematical expression for Boyle's law is:



               PV  k
where:
   P is the pressure of the gas
   V is volume of the gas

   k is a constant, and has units of force times distance
   Value of k is computed from measurements of volume and
    pressure for a fixed quantity of gas.
   The equation says that, after forcing the volume V of the fixed
    quantity of gas to increase, keeping the gas at the initially
    measured temperature, the pressure P must decrease
    proportionally. Conversely, reducing the volume of the gas
    increases the pressure.
   Boyle's law is commonly used to predict the result of
    introducing a change, in volume and pressure only, to the initial
    state of a fixed quantity of gas. The "before" and "after"
    volumes and pressures of the fixed amount of gas, where the
    "before" and "after" temperatures are the same (heating or
    cooling will be required to meet this condition), are related by
    the equation:
      Pafter  Vafter = Pbefore  Vbefore
   In practice, this equation is solved for one of the two "after"
    quantities to determine the effect that a change in the other
    "after" quantity will have. For example:
      Pafter = Pbefore  Vbefore / Vafter
                  Charles's law
Charles's law is one of the gas laws .

It states that “At constant pressure, the volume of a given
mass of an ideal gas increases or decreases by the same factor
as its temperature (in kelvins) increases or decreases” .
The mathematical expression for Charles's law is:


                  V
                    k
                  T
where:
      V is the volume of the gas
      T is the temperature of the gas (measured in kelvins)

      k is a constant
   To maintain the constant ,k ,during heating of a
    gas at fixed pressure, the volume must increase.
    Conversely, cooling the gas decreases the
    volume. The exact value of the constant need
    not be known to make use of the law in
    comparison between two volumes of gas at
    equal pressure:



   In simpler form, as the temperature increases
    the volume of the gas increases.
              Gay-Lussac's law
Gay-Lussac's law, known              as    the   law     of
combining volumes.

It states that “ At constant volume, the pressure of a fixed
mass of a given gas is directly proportional to the Kelvin
temperature”.
The mathematical expression for Gay-Lussac's law
is:

                  P
                    k
                  T
where:
          P is the pressure of the gas.
          T is the temperature of the gas (measured in kelvins).

          k is a constant.
This law holds true because temperature is a
measure of the average kinetic energy of a
substance; as the kinetic energy of a gas increases,
its particles collide with the container walls more
rapidly, thereby exerting increased pressure.

For comparing the same substance under two
different sets of conditions, the law can be written
as:
              Combined gas law
The combined gas law is a gas law which
combines Charles's law ,Boyle's law ,and Gay-
Lussac's law .In each of these laws ,pressure ,
temperature ,and volume ,respectively, must
remain constant for the law to be true. In the
combined gas law, any of these properties can be
found mathematically.

The law states that “The product of the volume of a gas
and its pressure over the temperature is equal to a constant”.
The mathematical expression for the combined law is:



                       PV
                          k
                       T
where:
           p is the pressure.
           V is the volume.

           T is the temperature (measured in kelvin in SI units).

           k is a constant
For comparing the same substance under two
different sets of conditions, the law can be written as:




We can however remove n (number of moles of the
gas) from the equation because it is constant when
changing only the conditions, to make:




The addition of Avogadro's law to the combined gas
law yields the ideal gas law.
                            Ideal Gas Law
The ideal gas law is the equation of state of a hypothetical ideal gas.

The state of an amount of gas is determined by its pressure, volume, and temperature according to
the equation:




where
                        PV  nRT
           the pressure [Pa],
         P is
      V is the volume [m3],
      n is the amount of substance of gas [mol],
      R is the gas constant 8.3143 m3·Pa·K-1·mol-1, and
      T is the temperature in kelvins [K].
The ideal gas constant (R) is dependent on what
units are used in the formula. The value given
above, 8.314472, is for the SI units of pascal-cubic
meters per mole-Kelvin .Another value for R is
0.082057 L atm per mol -Kelvin

The ideal gas law is the most accurate for
monatomic gases and is favored at high
temperatures and low pressures. It does not factor
in the size of each gas molecule or the effects of
intermolecular attraction.
             Example

A sample of chlorine gas weighs 1.31 g
at STP. Calculate the volume this
sample of chlorine would occupy
under the following new conditions:

3.20 atm and 0.0 C
                      Solution
   Calculate the moles of Cl2 from 1.31 grams = 0.0184
    moles Cl2
   Check the temperature and convert to Kelvin if
    necessary :K = C + 273 = 0.00 + 273 = 273 K
   Check the pressure given and convert to atmospheres
    unit. Pressure is already in atmospheres, 3.20 atm
   Use the value of R = 0.0821 liter-atm/mole-K
   Using the PV = nRT plug in the moles, temperature,
    pressure, and R and solve for the Volume in liters V =
    nRT / P = (0.0184 moles) ( 0.0821 liter-atm / mol-K)
    (273 K) / 3.20 atm = 0.129 liters
You try this:

A sample of chlorine gas weighs 1.31 g at STP.
Calculate the volume this sample of chlorine
would occupy under the following new
conditions:
 760 torr and -23.0 C
                          Solution
Calculate the moles of Cl 2 from 1.31 grams = 0.0184 moles Cl 2

Check the temperature and convert to Kelvin if necessary :K = C
+ 273 = -23.0 + 273 = 250 K

Check the pressure given and convert to atmospheres unit
.Pressure is in torr units and 1 atm = 760 torr units so 760 torr  1
atm / 760 torr = 1 atm

Use the value of R = 0.0821 liter-atm/mole-K

Using the PV = nRT plug in the moles, temperature, pressure,
and R and solve for the Volume in liters V = nRT / P = (0.0184
moles) ( 0.0821 liter-atm / mol-K) (250 K) / 1 atm = 0.378 liters
            Dalton's Law
In chemistry and physics, Dalton's
law (also called Dalton's law of
partial pressures) states that the total
pressure exerted by a gaseous
mixture is equal to the sum of the
partial pressures of each individual
component in a gas mixture.
Mathematically, the pressure of a mixture of gases
can be defined as the summation:




Where P1, P2, and P3 represent the partial pressure
of each component. It is assumed that the gases
do not react with each other.
Add partial pressures:
P1=n1RT/V
P2 =n2RT/V
P = (P1 +P2( = (n1 +n2 )( RT/V)

Add moles of each substance:
n = n1 +n2
P = (nRT/V( = (n1+n2) )RT/V(
                   Henry’s Law
In chemistry, Henry's law is one of the gas laws.
It states that:
“At a constant temperature, the amount of a given gas dissolved in
a given type and volume of liquid is directly proportional to the
partial pressure of that gas in equilibrium with that liquid”.

OR

“The Solubility of a Gas in a Liquid is Directly Proportional to
the Partial Pressure of the Gas above the Liquid”.
The Law can be represented by:

              Cequil  K H Pgas
Where
        Cequal = concentration of gas dissolved in the liquid
        at equilibrium
        Pgas = partial pressure of the gas above the liquid
        KH = Henry’s law constant for the gas at the given
        temperature
           Graham’s Law

The Law states that:

“The rate of diffusion of a gas is
inversely proportional to the square root
of its molecular weight”
The Law can be represented by:

                 t  MW
Where
        t = time required for diffusion
        MW = Molecular Weight

So          tA   MWA
               
            tB   MWB
A and B are gas A and gas B, respectively